A holographic lens, like any other hologram, can be described by its transmissivity t(x, y).

(a) What t(x, y) will take a reference wave, impinging from the θ_o direction (as in Fig. 10.8) and produce from it a primary object wave that converges on the spot (x, y, z) = (0, 0, d)?

(b) Draw a contour plot of the transmissivity t(x, y) of the lens in part (a). Notice the resemblance to the Fresnel zone plate of Sec. 8.4.4. Explain the connection of the two, paying attention to how the holographic lens changes when one alters the chosen angle θ_o of the reference wave.

(c) What t(x, y) will take a reference wave, impinging from the θ_o direction, and produce from it a primary wave that splits in two, with equal light powers converging on the spots (x, y, z) = (−a, 0, d) and (x, y, z) = (+a, 0, d)?

Figure 10.8.

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reference wave: Re-iksinyeik osz virtual image hologram: 7(x, y) = M² + O(x, y, z=0)²+O(x, y, z=0)Metiky sin + 0*(x, y, z = 0) Me-iky sin secondary real image reconstructed object wave: const x MRO(x, y, z)eik modulated mirror wave: const R(O2+ M²)e-ik sin foyek cos z phase conjugated object wave: const MRO*eiksin 8 yik cos